Secondary Imbibition in a Core Plug – Two-Phase Darcy’s Law

Figure 1. Mesh.

A water-wet vertical core plug initially saturated with oil is subjected to water injection from the bottom end, through a porous frit disc fully saturated with water and impermeable to oil. The core plug has a diameter of 1.0 inch and a length of 1.5 inch. Its absolute permeability and porosity values are 100 mD and 0.25, respectively. The residual water and oil saturations are Scw = 0.2 and Sor = 0.3, respectively; the initial water saturation of the plug is 0.22.
The system is at room temperature, and the density and viscosity values of the water and oil are ρw = 1.0 g/cc and ηw = 1.0 cP, and ρo = 0.85 g/cc and ηo = 3.0 cP, respectively.
The frit disc is 0.125 inch thick and has a permeability of 500 mD.
This two-dimensional model employs Cartesian coordinates.

The water saturation as function of the capillary pressure between the two liquids is given by a synthetic curve as shown in Figure 2. The relative permeability curves shown in Figure 3 are described by Corey relationships with Corey exponents of 5.0 and 2.5 for water and oil, respectively, while the end-point relative permeability values are krw_or = 0.25 and kro_cw = 0.7.
Gravity effects are included in the model.

Water injection occurs through the bottom boundary. The injection velocity is increased from zero at t = 0 to Vin = 13.2 micron/s in one minute, after which it is maintained constant (the value of Vin corresponds to an injection flow rate of five pore volumes per hour, for this two-dimensional geometry). The average water saturation Sw in the core plug as a function of time is plotted in Figure 4, while the distribution of Sw in the sample at selected time steps is shown through the Movie.

Figure 4. Average water saturation Sw in the core plug, as a function of time.Movie. Water saturation distribution in the core plug as a function of time.